# A nontrivial constant c=0.29795219028 in one and three dimensional random walks

Presented by:
S Majumdar Université Paris-Sud
Date:
Monday 26th June 2006 - 11:30 to 12:30
Venue:
INI Seminar Room 1
Abstract:

Two different random walk problems, one in one dimension and the other in three dimensions, seem to share a nontrivial constant whose numerical value is c=0.29795219028.. In the first problem, this constant shows up in the finite size correction to the expected maximum of a discrete-time random walk on a continuous line with unform jump density. In the second problem, this constant appears as the `Milne extrapolation length' in the expression for flux of discrete-time random walkers to a spherical trap in three dimensions. We prove why the same constant appears in the two problems and derive an exact analytical formula for this constant.

Presentation Material: